Energy Levels of an Ideal Quantum Ring in AA-Stacked Bilayer Graphene

TL;DR

This paper provides an analytical study of the energy spectrum of a quantum ring in AA-stacked bilayer graphene under magnetic fields, revealing unique symmetry properties and effects of applied potentials.

Contribution

It introduces an analytical Dirac-equation-based approach to analyze the energy spectrum of AA-stacked bilayer graphene quantum rings, highlighting symmetry breaking and potential-induced gap opening.

Findings

Energy spectrum exhibits hyperbolic dependence on magnetic field for fixed angular momentum.

Spectrum is not invariant under magnetic field reversal.

Applying a potential opens a gap and breaks symmetries.

Abstract

We theoretically analyze the energy spectrum of a quantum ring in AA-stacked bilayer graphene with radius $R$ for a zero width subjected to a perpendicular magnetic field $B$. An analytical approach, using the Dirac equation, is implemented to obtain the energy spectrum by freezing out the carrier radial motion. The obtained spectrum exhibits different symmetries and for a fixed total angular momentum $m$, it has a hyperbolic dependence of the magnetic field. In particular, the energy spectra are not invariant under the transformation $B \longrightarrow -B$. The application of a potential, on the upper and lower layer, allows to open a gap in the energy spectrum and the application of a non zero magnetic field breaks all symmetries. We also analyze the basics features of the energy spectrum to show the main similarities and differences with respect to ideal quantum ring in monolayer, AB-stacked bilayer graphene and a quantum ring with finite width in AB-stacked bilayer graphene.